Is it possible to get nx, ny, and nz values of an object's coordinates in blender?
Global representation of normal axes.

The global value of the  z axis z_axis = Vector((0, 0, 1)) of an object obj can be calculated using

nz = obj.matrix_world * z_axis


All can be calculated from the matrix world using,

nx, ny, nz =  [v.normalized() for v in obj.matrix_world.to_3x3().transposed()]